solving system application

Question

At a local amusment park it cost as fixed rate to park the car and a certain fee per person.One car entered with 3 passengers and paid $22. The next car had 5 passengers and paid $34. Find the cost of parking and cost per person.

Answer 1

One of the keys to solving any problem is to understand it,

and the old adage "a picture is worth a thousand words" is very appropriate.

So make a picture either by drawing a simple diagram or, in a case like this,

by making a chart that depicts the problem.

First - decide what type of problems it is.

Rate (or Value Cost), Value Mixture, Percent, Percent Mixture, Investment, ... etc.

This is a Rate Problem.

Second, know the basic formula for the type of problem.

The formula for this situation is similar to any rate problem.

Amount Χ Rate = Cost

But for this specific problem where there are two items being paid for,

Parking and People, you need to add the two items to get the total cost

just like you add all the things in your shopping cart at the grocery store.

Therefor the formula is:

( the Number of cars Χ the per car Parking rate )

plus

( the Number of people Χ the per person Entry rate )

equals the Cost

Third make the chart/diagram:

#cars Χ $ParkingFee + #people Χ $EntryFee = Cost

1 P 3 E $22

1 P 5 E $34

It is usually better NOT to use X and Y for the variables,

but instead to use letters that make sense so you will understand it.

You have two equations and two unknowns, P and E.

Solve the two simultaneous equations.

Answer 2

x=fixed rate to park

y=fee per person

x+5y=34

x+3y=22

subtract

2y=12

y=$6 per person

x+3*6=22

x+18=22

x=$4 parking fee